High-precision equation of state benchmark for cryogenic liquid deuterium at ultrahigh pressure

We provide a principal Hugoniot of cryogenic liquid deuterium at a pressure of $27<P<240$ GPa, with reflected-shock data of up to $\sim 830$ GPa. The maximum density reaches $\sim 1.49$ $\mathrm{g}/{\mathrm{cm}}^3$, about 8.7 times the initial density. Our independent principal Hugoniot experimental data broadly support the wide-regime equation of state (WEOS) model, which well matches Fernandez-Pañella et al. [Phys. Rev. Lett. 122, 255702 (2019)] and Knudson et al. [Phys. Rev. Lett. 118, 035501 (2017)] experimental data over the observed pressure range up to 550 GPa, and most of three sets of reflected shock data are in accordance with our theory up to 1 TPa. Our high-precision experimental results establish an important benchmark equation of state of deuterium and conform to the WEOS model quite well. Our work is useful for the development of the high-pressure response of hydrogen's isotopes, directly related to inertial confinement fusion, planetary science, and metallization.

Figure 1

(a) Real picture of the cryogenic deuterium target. (b) Schematic of the cryogenic deuterium target. (c) Raw VISAR image for shot 15035, showing continuous tracking of the shock front within both $D_2$ and $\alpha$-quartz. The corresponding velocity profile (green curve) is also shown.

Figure 2

Shock velocity vs particle velocity for the deuterium principal Hugoniot. Shown are the impedance-matching results for explosives from Ref. [49] (yellow diamonds), Ref. [50] (light cyan diamonds), and Ref. [18] (dark cyan diamonds); a gas gun from Ref. [16] (purple triangles); a magnetically driven flyer plate from Ref. [20] (gray squares) and Ref. [21] (blue squares); and laser-driven measurements from Ref. [51] (green circles), Ref. [22] (pink circles), and Ref. [23] (purple circles), and this work (red circles). The WEOS model (${\rho }_0=0.170$ $\mathrm{g}/{\mathrm{cm}}^3$; black solid line) is also shown.

Figure 3

Pressure vs compression plot of the principal Hugoniot of deuterium. Experimental data symbols are the same as in Fig. 2. All experimental data are plotted with error uncertainties. The data are compared to several EOS models: Kerley [37] (blue curve), Caillabet et al. [42] (green curve), FPEOS by Hu et al. [43] (pink curve), SESAME 5267 [39] (yellow curve), and WEOS (${\rho }_0=0.170$ $\mathrm{g}/{\mathrm{cm}}^3$; black curve) [45, 46].

Figure 4

Single-shock and reflected-shock pressure vs compressed densities of cryogenic liquid deuterium. Black circles correspond to single-shock data (Fig. 3). Stars correspond to $\left(P_1^{\mathrm{D}},{\rho }_1^{\mathrm{D}}\right)$ states from this work, the shocked state in $D_2$ prior to reflection by the quartz window (as the shock wave is not steady). Reshock states of deuterium from this work (solid circles) are shown. Dot-dashed lines are the WEOS model [45, 46] calculated from $P\left(U_{S1}^{\mathrm{D}}\right)$ of this work. The different colors of the $P_1^{\mathrm{D}}$ states and the reshock data represent different single-shock states. The dark gray dotted line is the WEOS model calculated by the impedance-matching technique with quartz.

Figure 5

$P\text{−}{u}_p$ diagram illustrating the impedance-matching technique.

Figure 6

Experimental observables for the reflected-shock experiments, $U_{S1}^{\mathrm{Q}}$ vs $U_{S1}^{\mathrm{D}}$, from this study are red solid circles. Previous $z$-pinch data from Knudson and Desjarlais [21] (gray squares) and laser-driven data from Boehly et al. [51] (green circles) and Fernandez-Pañella et al. [23] (purple circles) are also shown. All experimental data are plotted with error uncertainties. The colored solid lines correspond to the predictions of EOS models, which are the same as in Fig. 3. The velocity residuals of the different data sets and EOS models with respect to the WEOS model are shown in the top illustration. The initial density of the experiments in this work and the WEOS model is 0.170 $\mathrm{g}/{\mathrm{cm}}^3$, while other theoretical models quoted correspond to an initial density of 0.173 $\mathrm{g}/{\mathrm{cm}}^3$ [23].

Figure 7

$P_1^{\mathrm{D}}$ and reflected-shock pressure vs compressed densities of cryogenic liquid deuterium of (a) this work, (b) Fernandez-Pañella et al. [23], and (c) Knudson and Desjarlais [21]. The reshock states starting from various initial states $U_{S1}^{\mathrm{D}}$ of the three experiments are calculated with the WEOS model. The dark gray dotted line (black long-dashed lines) are the WEOS model (Caillabet et al.'s [42] model) calculated with the impedance-matching technique proposed by Fernandez-Pañella et al.

Figure 8

$P\text{−}\rho$ diagram illustrating the initial density effects of liquid deuterium.